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Observations on Business Cycle Accounting

Lawrence J. ChristianoJoshua M. Davis

Background• BCA: A strategy for identifying promising directions for

model development

• Fit simple RBC model to data

• Identify ‘wedges’

– Distortions between marginal rates of substitution in preferences and technology necessary to reconcile model and data.

• Decomposition:

– Simulate response of model to one wedge, holding other wedges constant.

– Compare results of simulation to actual business cycle data

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Papers on Business Cycle Accounting• Parkin, Michael, 1988, ‘A Method for Determining Whether

Parameters in Aggregative Models are Structural,’ Carnegie-Rochester Conference Series on Public Policy, 29, 215-252.

• Ingram, Beth, Narayana Kocherlakota and N. Savin, 1994, ‘Explaining Business Cycles: A Multiple-Shock Approach,’ Journal of Monetary Economics, 34, 415-428.

• Mulligan, Casey, 2002, ‘A Dual Method of Empirically Evaluating Dynamic Competitive Models with Market Distortions, Applied to the Great Depression and World War II,’ National Bureau of Economic Research Working Paper 8775.

• Chari, V.V., Patrick Kehoe and Ellen McGrattan, 2006, "Business Cycle Accounting," Federal Reserve Bank of Minneapolis Staff Report 328, revised February.

CKM’s Conclusion• Intertemporal wedge not important.

– accounts for only a small portion of business cycle contractions

– such wedges cannot be important, because they drive investment and consumption in opposite directions, while both these variables are procyclical in the data.

• Standard models of financial frictions (e.g. Carlstrom-Fuerst (CF) and Bernanke-Gertler-Gilchrist (BGG)) not useful directions for research.

• Results are insensitive to introduction of adjustment costs in investment.

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• CKM Finding Potentially of Major Interest

– Early phases of US Great Depression accompanied by major decline in the stock market and unusually massive decline in investment

– 2000 recession associated with stock market crash and unusually large drop in investment

– Researchers Infer from observations like these that financial market imperfections as in CF and BGG are important in business cycles

• CKM conclude this is a waste of time

Our Findings:• BCA may greatly understate the importance in business cycles of

financial frictions like those of CF or BGG.

– Financial frictions likely to generate spillover effects onto other wedges, and these are ignored in BCA.

– The precise magnitude of spillovers is not identified under BCA, because this requires pinning down the fundamental shocks to the economy. These are not identified under BCA.

• CKM conclusions relative to US and several other countries are not robust to introduction of adjustment costs in investment.

– A full reconciliation in results with CKM is still being worked on.

– One factor: CKM adopt a particular measurement error scheme during estimation of their model on US data. We show this scheme is overwhelmingly rejected, and it leads to points in the parameter space where adjustment costs seem not to matter much.

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Intertemporal wedge

Labor wedge

Efficiency wedge

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Outline• Distinction between fundamental economic shocks and ‘wedges’

– Economic shocks originate inside wedges and spill over into other wedges

– Wedges are correlated

• Illustrate intertemporal wedge.

• Display law of motion of wedges.

• Argument in favor of including investment adjustment costs in anRBC model.

• Explain a priori reasons that adjustment costs might be important in assessing importance of intertemporal wedge.

• Go for the basic results

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Individual capital producers arecompetitive and have linear homogeneoustechnologies. They take prices parametrically. In equilibrium, market price ofnew capital must equal marginal cost. With moInvestment, equilibrium price of new capital rise

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• Following is the law of motion for the wedges.

• We follow CKM in allowing virtually unrestricted correlation among wedges.

• This is consistent with the sort of models BCA is designed to shed light on: even though fundamental economic shocks may be independent, wedges will not necessarily be independent

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A Case for Adjustment Costs

• The standard RBC model’s implications for rates of return are strongly counterfactual

• Adjustment costs improve those implications

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• Rate of return to capital:

1 Rt1k

MPk,t1Pk,t1

Pk ′,tadjustment costs

MPk,t1 1 − no adjustment costs

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We go with this elasticity. Could go smaller.

Standard RBC model…

Why Would Adjustment Costs Matter?

• Consider intertemporal Euler equation:

• Suppose varies very little in the absence of adjustment costs

– When you add adjustment costs, fluctuates more and – assuming fluctuations in do not change, this requires variance of to increase.

1 Etmt11−t1k Rt1

k ,

t1k

Rt1k

mt1 t1

k

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Next:

• Solution of the Model

• Parameter Estimation

• Interesting Property of Solution: VAR Representation

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Identifying the Contribution of Financial Frictions to Business

Cycle Dynamics• Financial Frictions:

– Source of shocks (e.g., monitoring and risk shocks)• operate through two channels:

– intertemporal wedge– Spillovers onto other wedges

– Source of propagation of other shocks ( technology, government spending, etc.)

• those shocks spill over onto the intertemporal wedge

– Requires isolating fundamental shocks, but this is impossible under BCA.

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The identification problem:each value of θ gives rise to a different specification of the fundamentalshocks, yet the second momentproperties of the model are unaffected.

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Original system

Part of system thatcorresponds to financial frictions

Direct effect of financial shock onintertemporal wedgeSpillover effects of financial friction shocks

Spillover of other shocks onIntertemporal wedge

Financial shock

Intertemporalwedge

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Time Series Representations for Wedges

• Full moving average representation of wedges:

• Moving average representation of wedges when only effects of financial frictions are allowed to operate

st FLt

st FLt

Time Series Representations for Observed Data

• Observer equation:

• Or, in compact notation:

• Representation of data which isolates financial frictions

Y t h 0 s t h 1 lo g k t t h 0 h 1 L

1 − L s t t

h 0 h 1 L

1 − L s t t

Y t HLFL t t .

Yt HLFLt t, HL h0 h1L

1 − L

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A Measure of the Importance of Financial Frictions

• Statistic:

• This object is a function of θ

– Importance of Financial Frictions Not Identified

f varHLFLt

varHLFLt t

Identifying the Role of Financial Frictions in the Data

• CKM approach (I’m oversimplifying)– Determine recession periods.– Feed the measured intratemporal wedge to the

model, holding the other wedges fixed at their values at the start of the recession

• This may understate the role of financial frictions, to the extent that there are spillover effects from financial shocks to other wedges.

Yt h0st h1 logkt tlogk t1 logkt st

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Alternative Strategy Which Allows for Spillovers

• Choose θ to maximize statistic, f

• Simulate response of data to financial shock only.

– This understates importance of financial frictions to the extent that non-financial shocks move the intertemporal wedge

– Our way of choosing θ mitigates this problem.

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Message: when the (statistically rejected) model of measurement error is dropped, anda conservative amount of adjustment costs areused, CKM measure of importance of intertemporal wedge is big (let column). With spillovers, financial frictions could be EVERYTHING

Notehowinvestand consmovein opp.direct.

With spilloverC andI move in samedirect.

Fraction of drop in output at trough accounted forBy wedge

Percent decline in output at trough of recession, averaged over 5 US recessions,due to intertemporal wedge: adjustment costs make no difference to this quantitywhich is not huge.

Allowing for spillovers from financial shocks to other wedges hasa huge impact on contribution of financial shocks to business cycles

When CKM’s (overwhelmingly rejected) model of measurement error is dropped, adjustment costs are very important though even CKM’s own measure indicates financial frictions are important when there are adjustment costs

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No adjustment cost case

Strong rejection – against alternative of no measurement error - of CKM model of measurement error for all countries but France and Germany. If the CKM model where ‘true’ the test statistic would be a chi-square with four degrees of freedom.

With no measurementerror and no adjustmentcosts, financial frictions predict booms during Recessions.

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Conclusion• Key Conclusion of CKM Analysis: Financial Frictions that Enter

Intertemporal Euler Equation Not Important for Understanding Business Cycles.

• With adjustment costs in investment and dropping CKM’s rejected model of measurement error, we find:

– Financial frictions important in the US, even without allowing for spillovers from financial shocks to other wedges

– Accounting for spillovers, there is no expectation that financial friction shocks drive consumption and investment (counterfactually) in opposite directions.

– Allowing for spillovers, the business cycle effects of financial frictions are potentially huge.

• There is nothing in Business Cycle Accounting to warrant abandoning models of financial frictions which distort intertemporal margins (e.g., the CF and BGG models).

Appendix Figures

• Following figures report Figures 1 and 2 for four other US recession episodes.

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